Microchannel devices are finding increased use in the separation, identification and synthesis of a wide range of chemical and biological species. Employing transverse channel dimensions in the range from a few microns to about one millimeter, such systems may permit the miniaturization and large-scale integration of many chemical processes in a manner analogous to that already achieved in microelectronics. Applications for microchannel devices now under development include such diverse processes as DNA sequencing, immunochromatography, the identification of explosives, identification of chemical and biological warfare agents, and the synthesis of chemicals and drugs.
In addition to the potential for large-scale integration, the small physical scales of microchannel devices offer a few inherent advantages over their traditional macro-scale counterparts. Traditional chromatographic separations are usually performed in packed columns. The role of the packing is to provide a stationary phase having a large specific surface area for the adsorption of chemical species. Since various chemical species have different absorption probabilities and residence times on the stationary phase, they move with different speeds through the column and thus exhibit a range of arrival times at the column exit. Although larger surface areas provide better separation between arrival times, the use of packing materials causes nonuniformity of the fluid motion. This results in hydrodynamic dispersion of the solute bands or peaks used to distinguish the species. The benefit of the packing material is thus partially offset by the detriment of increased dispersion. This compromise can be avoided at the smaller scale of microchannel devices. Since the specific surface area of a tube or channel is inversely proportional to its minimum transverse dimension, microchannel columns may provide the required surface area without any need for a packing.
One promising method of microchannel separation is electrochromatography in which electric fields are used to drive electroosmotic fluid motion. Such fluid motion results from the applied electric field acting on charges in the electric Debye layer adjacent to the tube or channel walls, inducing a shear stress very near the boundary of the interior fluid. Electroosmotic flows offer two important benefits over pressure-driven flows for the small physical dimensions characteristic of microchannel devices. First, fluid speeds in electroosmotic flows are independent of the transverse tube or channel dimension over a wide range of conditions, making this technique extensible to extremely small physical scales. In contrast, pressure-driven flows require a pressure gradient that increases inversely with the square of the minimum transverse dimension to maintain a given fluid speed.
Another promising approach to micro-scale chemical analysis is electrophoretic separation. Here the carrier fluid may be either moving or nearly stationary, and an applied electric field is used to drive ionic species through a gel or liquid. Separation occurs because the ion speeds depend on the unique charge and mobility of each species. Provided that the applied field is uniform across the tube or channel cross-section, all ions of the same charge and mobility move at the same speed and so progress along the column without any induced dispersion. Such motion is analogous to the flat velocity profile of an electroosmotic flow, and the various species thus again exhibit unique arrival times at the column exit. Like electrochromatographic processes, electrophoretic separations may be severely degraded by diffusion or dispersion. In the latter case, however, dispersion may arise not only from nonuniformity of the carrier fluid speed but may also arise directly from nonuniformity of the electric field across the column cross-section.
Although species motion in both electrophoretic and electroosmotic transport may be relatively free of both diffusive and dispersive spreading in straight tubes or channels having parallel walls, any local variation in the fluid speed or local field strength introduces dramatic skewing of an otherwise flat interface or species band. Such skewing is known to occur within a separation structure wherein the fluid channel includes bends, or xe2x80x9cturns,xe2x80x9d typically used to extend the length of the channel within a fixed area. Skewing is induced along the radius of the turn because the fluid moving along the outer radius of a turn must travel further than that moving along the inner radius. This difference in path length is compounded by the electric field gradient which is greater along the shorter inner radius, resulting in a greater fluid speed along the shorter path. Thus, an initially flat interface will be severely skewed in passing through a turn. Moreover, because transverse diffusion quickly redistributes solute concentrations across the channel, such skewing is irreversible, and the net effect of transport through any turn or other junction is a large and permanent broadening of any solute peak or interface. As a result, separations are presently performed in straight channels that are limited in length by the maximum substrate dimension. This restriction limits the separation between peaks traveling at different speeds and, so, limits the resolution of separation devices.
Turns are a well-known source of dispersive band spreading in microchannel systems employing electrokinetic species transport. This spreading impairs performance in separation processes, as well as in routine sample transport where the integrity of a band or interface is desired. As a result, turns are often avoided in microchannel system design, especially in the layout of separation columns.
Several previous studies have examined the character and extent of band spreading in turns. Kasicka, et al. (Electrophoresis, v16, 1995, pp. 2034-2038) analyzed the effects of capillary coiling on capillary zone electrophoresis. This study focused on cases in which transverse diffusion is negligible, and the authors obtained closed-form expressions describing the increased variance of the species distribution induced by a turn. Culbertson, et al. (Anal. Chem., v70, 1998, pp. 3781-3789) investigated several sources of dispersion in microchannel devices. As part of this study, they collected a large set of data on the increased variance of a species band downstream of a turn. They also developed a physically-motivated expression describing the increased variance, taking into account both diffusive and convective species transport. More recently, Griffiths and Nilson (Anal. Chem., v72, 2000, pp. 35473-5482) derived a closed-form expression for the increased band variance induced by a turn. This expression was obtained from solutions to the transport equations in the limits of low and high Peclet numbers, again taking into account both diffusion and convection as appropriate.
A few previous studies also have dealt specifically with remedies to turn-induced spreading. Paegel, et al.( Anal. Chem., v72, 2000, pp. 3030-3037) proposed narrowing the channel width upstream of a turn followed by widening the channel once the turn is completed. This approach takes advantage of the fact that the dispersive portion of the increased band variance due to a turn is proportional to at least the square of the channel width. Reducing the channel width throughout the span of the turn thus reduces band spreading. By properly sizing the length and extent of the tapered sections before and after the turn, the authors demonstrated separation efficiencies in folded columns approaching those of a straight separation column of equal length. In contrast, Griffiths and Nilson (Anal. Chem., v73, 2001, pp. 272-278) developed low-dispersion turns based on geometries that counter-rotate the band before and after the turn. These low-dispersion geometries, discerned by means of computer optimization, yield an increased band variance two to three orders of magnitude below that of an equivalent conventional turn, while requiring only moderate constriction of the channel width.
Although special turn geometries offer very significant improvement over conventional turns of similar radius, such enhanced performance is not always required. Large-radius turns of fixed channel width may yield satisfactory performance, so long as the Peclet number is sufficiently small. Recognizing this fact, Culbertson, et al. (Anal. Chem., v72, 2000, pp. 5814-5819) devised a spiral separation column having a large turn radius. This spiral geometry provides a means to construct a very long column within a relatively small chip area, despite the large turn radius. These authors, therefore, successfully demonstrated separation efficiencies that were degraded only slightly by the spiral geometry for a channel width of 40 xcexcm, a minimum turn radius of about 16 mm and Peclet numbers up to about 400.
We have examined the spreading of a species band traversing a two-dimensional microchannel turn and an adjoining straight channel segment. The width of the turn and straight segment are assumed to be uniform. Closed-form solutions are obtained describing the minimum turn radius such that dispersive band spreading in the turn is negligible compared to the overall spreading due to diffusion in the turn and straight segment. This minimum radius depends in general on the channel width, included turn angle, the Peclet number and the length of the straight channel segment.
We find that a straight channel segment adjoining a turn significantly reduces the minimum turn radius, provided that the segment length is sufficient: some reduction in the minimum radius can be obtained even when the straight segment length is smaller than the turn radius. Folded separation columns containing straight channel segments may thus employ turns having radii smaller than the minimum radius for a spiral geometry, without degrading the resolution of separation processes.
Based on these results, we have devised new geometries for the compact layout of separation columns. These rely on the benefit of using straight channel segments in conjunction with turns in order to reduce the turn radius. The first geometry is a pleated column, similar to a conventional folded column, in which opposing turns are overlapped to reduce the occupied chip area by about a factor of two below that required for the conventional folded geometry. The second and third are coiled and double-coiled geometries in which the turns are nested. The coiled column has one end that terminates within the coil, while both ends of the double-coiled column terminate outside. Using the double-coiled geometry, a separation column having a 40 xcexcm width and 210 mm length can be placed in a region just 13 by 42 mm. The total length can be extended by about 100 mm for each 2 mm increase is the width and height of this region. The performance of this column is comparable to that of a straight column of equal length for Peclet numbers up to 400.